8x8 Queens Puzzle #293
Difficulty: medium. Place 8 queens on this 8x8 board so that no two share a row, column or color region and none touch — including diagonally. This puzzle has exactly one solution, and it has been verified solvable by deduction alone: the complete 8-step reasoning is written out below.
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Step-by-step solution for puzzle #293
What follows is a complete solve of puzzle #293, worked the way a person works it rather than the way a computer does. It runs to 8 deductions, every one of them a forced placement. Each step names the rule that forces it, so nothing below is a guess, and the hardest idea required is the last square in a region.
Techniques this board needs: last square in a region.
Show the full walkthrough (8 steps) — contains the solution
Step 1. Only row 5, column 4 is still open in slate, and since each colour must take a queen, that settles it. That clears row 5, column 4, the rest of the slate region and every square adjacent to it — diagonals included.
Step 2. The blue region is down to one open square, at row 3, column 3. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 3 and column 3, the remaining blue squares, and the ring of neighbours around row 3, column 3.
Step 3. Only row 8, column 8 is still open in khaki, and since each colour must take a queen, that settles it. Everything else in row 8, in column 8, in khaki and in the ring around that square is now dead.
Step 4. The mint region is down to one open square, at row 4, column 7. Every colour holds exactly one queen, so that square is forced. Row 4 and column 7 are now spoken for, along with the squares touching that queen.
The board after step 4 — 4 of 8 queens placed. Step 5. Only row 2, column 1 is still open in amber, and since each colour must take a queen, that settles it. That clears row 2, column 1, the rest of the amber region and every square adjacent to it — diagonals included.
Step 6. The red region is down to one open square, at row 6, column 6. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 6 and column 6, the remaining red squares, and the ring of neighbours around row 6, column 6.
Step 7. Only row 1, column 5 is still open in indigo, and since each colour must take a queen, that settles it. Everything else in row 1, in column 5, in indigo and in the ring around that square is now dead.
Step 8. The pale yellow region is down to one open square, at row 7, column 2. Every colour holds exactly one queen, so that square is forced. Row 7 and column 2 are now spoken for, along with the squares touching that queen.
The board after step 8 — 8 of 8 queens placed.
That completes the board: 8 queens seated, one in every row, one in every column and one in every colour, with no two of them touching. Notice that nothing in the sequence above required a guess — each placement followed from an elimination already on the grid, which is what “single solution, solvable by logic” actually means in practice.
About 8x8 Queens puzzle #293
Puzzle #293 is one of the medium-rated boards in the 8x8 set. Eight colors divide its 64 squares, and you win by placing eight queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.
There is exactly one way to finish #293, and it has been verified. More importantly, you can reach it without ever gambling: at every stage some square is provably right or provably wrong. Boards differ only in how deep you must dig before that proof appears, and the geometry of these eight regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #293 are: slate (1 square), khaki (1 square), blue (5 squares), amber (6 squares), mint (10 squares), red (10 squares), indigo (15 squares), pale yellow (16 squares). An even split would hand every color 8 squares, so the slate region is running 7 squares under that average while the pale yellow region is the roomiest area on the grid with 16 squares.
Why does the split matter? Because a region's square count has no bearing on how many queens it gets — the answer is always one. So slate, with 1 square, is under far more pressure than pale yellow with 16. A 15-square gap like this one rewards players who start where the choices are fewest.
Look at arrangement as well as area. Slate is the densest region on this grid at 100% of a 1×1 frame; red is the loosest, occupying only 50% of its 5×4 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
Region by region
Each region's exact extent on this grid is listed below, starting with the most constrained. Knowing which lines a color can and cannot reach is most of the work on a medium board.
Slate occupies 1 square within rows 5–5, columns 4–4. It never leaves row 5, so its queen is locked to that row.
Khaki: 1 square across rows 8–8, columns 8–8. It never leaves row 8, so its queen is locked to that row.
Blue covers 5 squares, spanning 2 rows and 3 columns (rows 3–4, columns 3–5).
Amber occupies 6 squares within rows 2–5, columns 1–2.
Mint: 10 squares across rows 1–7, columns 7–8.
Red covers 10 squares, spanning 5 rows and 4 columns (rows 4–8, columns 4–7).
Indigo occupies 15 squares within rows 1–3, columns 1–7.
Pale yellow: 16 squares across rows 5–8, columns 1–6.
Where to start on this board
Open on the tightest color. Here that is slate, confined to 1 square between rows 5 and 5 and columns 4 and 4. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #293.
Because slate never leaves row 5, its queen must be in that row — and that instantly settles row 5 for everyone else. Sweep along it and X out every square that is not slate. Then look at which colors just lost ground: on a grid this size that one observation usually forces a second region within a move or two.
Work outward to the other flat regions next. Khaki and blue are no more than two rows tall, so their queens are confined to a narrow band. When two flat regions overlap the same pair of rows, those rows are spoken for and every other color is locked out of both — the single most productive pattern in the game, and it is live on this board.
The tightest lines on puzzle #293
A quick way to find the next move is to count how many different colors touch each line. On this board, row 1 is the narrowest, touched by only 2 colors. Column 8 is the tightest column, with 2 colors.
A line with few colors is a line close to resolving. Where only 2 colors appear, one of them owns the row outright and the others must fit into the remaining 7 rows. Row 5 is the crowded extreme at 5 colors — worth revisiting later, not now.
Working through the middle game
The middle of #293 is where careless play costs time. Every queen you place kills a row, a column and the eight surrounding squares; if you do not mark all of that immediately, you will later "discover" a move that was available several turns ago. Mark first, then look.
Two checks, run alternately, will carry you through the 64 squares of this grid. First: has any of the eight regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 8x8 boards almost always run one of those checks and forget the other.
Resist the plausible-looking queen. On #293 every correct placement has a stated reason behind it, and any move you cannot justify is a guess wearing a disguise. Backing out of a wrong guess on a single-solution board takes far longer than finding the real deduction would have.
Why puzzle #293 is rated medium
The medium label comes out of four measurable things about #293: four of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 2 colors, and its largest and smallest regions differ by 15. Boards that score tight on those measures give up their first queen fast.
Difficulty in Queens is never arithmetic and never luck. Every board has one solution and none require guessing. What varies is the length of the chain you must follow before the next queen becomes certain — one or two steps on an easy board, five or six on a hard one, sometimes with several partial eliminations held in play at once.
Stuck on #293 despite the medium rating? The odds strongly favour a bookkeeping error over a hard chain of logic. Re-check each placed queen for its complete set of eliminations, paying particular attention to the four diagonal squares — those are the ones that get overlooked, and one of them is usually sitting on the answer.
Techniques that work well at 8x8
At 8x8 the whole grid stays within a single glance, which makes systematic scanning practical. Read the rows in order and count the colors in each — a row touched by two colors is far more constrained than one touched by five, and that is usually where the next forced move hides. The board is small enough that re-scanning from the top after each placement costs almost nothing.
Learn the pairing argument and you will use it on every board, this one included. If two colors can only sit inside the same two rows, between them they consume both rows and every other color is shut out. It generalises to any matching count — three colors across three rows, four across four. On #293, start hunting for it near row 1.
A non-spoiling distribution check: solved, #293 carries 3 queens on the perimeter against 5 queens inside, 1 of them cornered. Because no two queens may touch, real solutions always look fairly evenly spread — a lopsided board in progress is a warning sign.
How to play Queens
- The board is an N×N grid divided into N colored regions.
- Place exactly one queen (♛) in each row, each column, and each colored region.
- No two queens may touch each other — not horizontally, vertically, or diagonally.
- Tap once to mark a square with an X (where a queen can't go), tap again to place a queen, and once more to clear it.
- There is always exactly one valid solution. Use logic, never guessing, to find it.
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Questions about this puzzle
How hard is 8x8 Queens puzzle #293?
Puzzle #293 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and four of its regions are confined to a single row or column, which gives you a forced move early.
Does 8x8 puzzle #293 have only one solution?
Yes. Every puzzle in the 8x8 collection, including #293, has been verified to have exactly one valid arrangement of eight queens, and it can always be reached by logic alone — no guessing or backtracking needed.
Where should I place my first queen on puzzle #293?
Start with the slate region — the most constrained color on this board, with 1 square spanning rows 5–5 and columns 4–4. Narrowing the smallest region first removes the most squares elsewhere on the grid.